Here's the thing about Border Collies. They are working dogs. Big time. One of the best working dogs that exists. They are obsessive about their work, actually. So needless to say, a Border Collie must be kept very busy with "work" or they will likely get themselves into trouble. Because if they're not *also compulsively* taught exactly what the expectation is and overseen continuously, they can take matters into their own hands.
So while it's great to get a trainer, what your daughter needs to do if she's going to safely keep this dog is to make a committment to "retraining" her and committing to keeping her busy and supervising her at all times. She should also read up on Border Collies in a big way (as should you as long as the dog is in your home - there is plenty of information available on the Net). The dog will likely
never be good around children at this point, because (and remember, she's extremely smart) she's learned (on first bite) and it's been reinforced (on second bite) that she can bite a child and the child will go away. In his mind, he's got it all figured out.
A friend of ours owns, breeds and works Border Collies. He has had some that were not good with children, and those dogs were kept away from them, plain and simple. When they were not working they were kept in a large pen. Your DD has GOT to be smart about this. I'm not sure how old she is but she sounds like she's probably late teens or early 20s? Probably working or going to school? Realistically, if she's going to keep this dog, she needs to be working the dog HARD. A dog like this needs to channel its energy. Many people do frisbee or agility or ball playing or something like that, and not just a few tosses. Along with that, there'd need to be SMART supervision and keeping the dog away from children forever, and that means even on walks at the park and such. Your DD needs to really take a close look at that to see if she can manage it. Because if she can't, there will be more trouble. A dog like this laying around all day doing nothing is asking for trouble. I can assure you it will keep itself busy. A trainer will not change these facts, just help your DD to see them.
I do wish you well. It's a difficult situation, but it unfortunately - at least the second bite - probably could have been avoided. Everyone in your household needs to understand that the dog should be safely put away before any children or other strangers come into the house - every. single. time. If you don't have a crate you should get one. This is the safest place (as opposed to behind a door that could be opened; or outside when the dog could get back in, etc).